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• CommentRowNumber1.
• CommentAuthorTodd_Trimble
• CommentTimeJul 22nd 2013

I’ve been adding a considerable amount of detail to relational beta-module. Not quite finished, but a lot of former ellipses have been filled in, and technical results proved from scratch.

If anyone knows this material, I’d enjoy hearing of any proposed simplifications. My local university library does not have the Springer Lecture Notes where Barr first wrote his article on relational beta-modules, and it’s hard finding detailed material at this ground level on the internet, so this represents pretty much what I’ve been able to work out by myself. (And it might read that way.)

• CommentRowNumber2.
• CommentAuthorTobyBartels
• CommentTimeJul 23rd 2013

Nice work! I haven't read it over and won't have time until next month, but it looks good.

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeJul 23rd 2013

Yes, this looks very nice indeed.

• CommentRowNumber4.
• CommentAuthorTodd_Trimble
• CommentTimeJul 27th 2013

Thanks, guys. Almost finished with relational beta-module; the main tasks have now been completed (after the considerable trouble I had in nailing down the details of theorem 3, which seems, weirdly, not very hard in hindsight).

I’m having weird troubles with the syntax in linking to a previous section. I tried creating such a link within the proof of theorem 2, following the instructions in HowTo to the letter, or at least so I thought, but something’s getting messed up (look at the address which appears when you hover over the link called “previous section” – clicking sends you to an uncreated page, and I’m worried now about the dreaded cache bug). Toby I know is on vacation, but someone knowledgeable might be able to step in and sort things out.

• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeJul 28th 2013

I think you’re missing a forward slash at the beginning of the URL /nlab/show/....

• CommentRowNumber6.
• CommentAuthorTodd_Trimble
• CommentTimeJul 28th 2013

Well, I’ll be damned. Thank you so much! That was it all right.

• CommentRowNumber7.
• CommentAuthorTodd_Trimble
• CommentTimeAug 4th 2013
• (edited Aug 4th 2013)

Okay, I’ve now added some detailed material on the generalized multicategory point of view on relational beta-modules.

I think this is a useful thing, because by focusing on this special case, one can streamline through a lot of complications and still give at least some taste of the very general Cruttwell-Shulman theory (which we should probably have more details on in the nLab, but it’s not an easy story to write down details for).

• CommentRowNumber8.
• CommentAuthorMike Shulman
• CommentTimeAug 5th 2013

Nice! Thanks!